| Quantal interferometry with dissipative internal motion - Erik Sjöqvist In presence of dissipation, quantal states may acquire complex-valued phase effects. We suggest a notion of dissipative interferometry that accommodates this complex-valued structure and that may serve as a tool for analyzing the effect of certain kinds of external influences on quantal interference. The concept of mixed-state phase and concomitant gauge invariance is extended to dissipative internal motion... Downloads: 8 | |

| Experimentally testable geometric phase of sequences of Everett's relative quantum states - Erik Sjöqvist Everett's concept of relative state is used to introduce a geometric phase that depends nontrivially on entanglement in a pure quantum state. We show that this phase can be measured in multiparticle interferometry. A correlation-dependent generalization of the relative state geometric phase to mixed quantum states is outlined. Downloads: 4 | |

| Pancharatnam revisited - Erik Sjöqvist Some recent ideas concerning Pancharatnam's prescription of relative phase between quantal states are delineated. Generalisations to mixed states and entangled two-photon states are discussed. An experimental procedure to test the geometric phase as a Pancharatnam relative phase is described. We further put forward a spatial split-beam dual to Pancharatnam's relative phase. Downloads: 6 | |

| On geometric phases for quantum trajectories - Erik Sjöqvist A sequence of completely positive maps can be decomposed into quantum trajectories. The geometric phase or holonomy of such a trajectory is delineated. For nonpure initial states, it is shown that well-defined holonomies can be assigned by using Uhlmann's concept of parallel transport along the individual trajectories. We put forward an experimental realization of the geometric phase for a quantum trajectory in interferometry... Downloads: 3 | |

| Dali Lapithos DII 1 D - Erik Sjöqvist Diary from the Swedish Cyprus Expedition. Medelhavsmuseet. Keywords: Journal; Logbook; akropol; arkeologi; Cypern; Lapithos; Plakes; Medelhavsmuseet Downloads: 59 | |

| Geometric phase in weak measurements - Erik Sjöqvist Pancharatnam's geometric phase is associated with the phase of a complex-valued weak value arising in a certain type of weak measurement in pre- and post-selected quantum ensembles. This makes it possible to test the nontransitive nature of the relative phase in quantum mechanics, in the weak measurement scenario. Downloads: 20 | |

| On the alleged nonlocal and topological nature of the molecular Aharonov-Bohm effect - Erik Sjöqvist The nonlocal and topological nature of the molecular Aharonov-Bohm (MAB) effect is examined for real electronic Hamiltonians. A notion of preferred gauge for MAB is suggested. The MAB effect in the linear + quadratic $E\otimes \epsilon$ Jahn-Teller system is shown to be essentially analogues to an anisotropic Aharonov-Casher effect for an electrically neutral spin$-{1/2}$ particle encircling a certain configuration of lines of charge. Downloads: 6 | |

| Lapithos DII 1 A - Erik Sjöqvist Diary from the Swedish Cyprus Expedition. Keywords: Lapithos; Vrysi tou Barba; Necropolis Downloads: 66 | |

| Entanglement-induced geometric phase of quantum states - Erik Sjöqvist The concept of relative state is used to introduce geometric phases that originate from correlations in states of composite quantum systems. In particular, we identify an entanglement-induced geometric phase in terms of a weighted average of geometric phase factors associated with a decomposition that define the entanglement of formation. An explicit procedure to calculate the entanglement-induced geometric phase for qubit pairs is put forward... Downloads: 7 | |

| Comment on "Geometric phases for mixed states during cyclic evolutions" - Erik Sjöqvist It is shown that a recently suggested concept of mixed state geometric phase in cyclic evolutions [2004 {\it J. Phys. A} {\bf 37} 3699] is gauge dependent. Downloads: 6 | |

| Kastros 1927 DII 1 B - Erik Sjöqvist Diary from the Swedish Cyprus Expedition. Keywords: Kastros Downloads: 65 | |

| Optimal Topological Test for Degeneracies of Real Hamiltonians - Niklas Johansson We consider adiabatic transport of eigenstates of real Hamiltonians around loops in parameter space. It is demonstrated that loops that map to nontrivial loops in the space of eigenbases must encircle degeneracies. Examples from Jahn-Teller theory are presented to illustrate the test. We show furthermore that the proposed test is optimal. Downloads: 3 | |

| Quantum computation using the Aharonov-Casher set up - Marie Ericsson It is argued that the Aharonov-Casher set up could be used as the basic building block for quantum computation. We demonstrate explicitly in this scenario one- and two-qubit phase shift gates that are fault tolerant to deformations of the path when encircling two sites of the computational system around each other. Downloads: 4 | |

| Weak cloning of an unknown quantum state - Erik Sjöqvist The impossibility to clone an unknown quantum state is a powerful principle to understand the nature of quantum mechanics, especially within the context of quantum computing and quantum information. This principle has been generalized to quantitative statements as to what extent imperfect cloning is possible. We delineate an aspect of the border between the possible and the impossible concerning quantum cloning, by putting forward an entanglement-assisted scheme for simulating perfect cloning in... Downloads: 6 | |

| Relative state measures of correlations in bipartite quantum systems - Pierre Rudolfsson Everett's concept of relative state can be viewed as a map that contains information about correlations between measurement outcomes on two quantum systems. We demonstrate how geometric properties of the relative state map can be used to develop operationally well-defined measures of the total correlation in bipartite quantum systems of arbitrary state space dimension. These measures are invariant under local unitary transformations and non-increasing under local operations... Downloads: 4 | |

| Hidden parameters in open-system evolution unveiled by geometric phase - Patrik Pawlus We find a class of open-system models in which individual quantum trajectories may depend on parameters that are undetermined by the full open-system evolution. This dependence is imprinted in the geometric phase associated with such trajectories and persists after averaging. Our findings indicate a potential source of ambiguity in the quantum trajectory approach to open quantum systems. Downloads: 4 | |

| Searching for degeneracies of real Hamiltonians using homotopy classification of loops in SO($n$) - Niklas Johansson Topological tests to detect degeneracies of Hamiltonians have been put forward in the past. Here, we address the applicability of a recently proposed test [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] for degeneracies of real Hamiltonian matrices. This test relies on the existence of nontrivial loops in the space of eigenbases SO$(n)$. We develop necessary means to determine the homotopy class of a given loop in this space... Downloads: 18 | |

| Precession and interference in the Aharonov-Casher and scalar Aharonov-Bohm effect - Philipp Hyllus The ideal scalar Aharonov-Bohm (SAB) and Aharonov-Casher (AC) effect involve a magnetic dipole pointing in a certain fixed direction: along a purely time dependent magnetic field in the SAB case and perpendicular to a planar static electric field in the AC case. We extend these effects to arbitrary direction of the magnetic dipole. The precise conditions for having nondispersive precession and interference effects in these generalized set ups are delineated both classically and quantally... Downloads: 5 | |

| Geometry of decomposition dependent evolutions of mixed states - David Kult We examine evolutions where each component of a given decomposition of a mixed quantal state evolves independently in a unitary fashion. The geometric phase and parallel transport conditions for this type of decomposition dependent evolution are delineated. We compare this geometric phase with those previously defined for unitarily evolving mixed states, and mixed state evolutions governed by completely positive maps. Downloads: 9 | |

| Mixed state non-Abelian holonomy for subsystems - Mikael Nordling Non-Abelian holonomy in dynamical systems may arise in adiabatic transport of energetically degenerate sets of states. We examine such a holonomy structure for mixtures of energetically degenerate quantal states. We demonstrate that this structure has a natural interpretation in terms of the standard Wilczek-Zee holonomy associated with a certain class of Hamiltonians that couple the system to an ancilla... Downloads: 6 | |

| Off-diagonal generalization of the mixed state geometric phase - Stefan Filipp The concept of off-diagonal geometric phases for mixed quantal states in unitary evolution is developed. We show that these phases arise from three basic ideas: (1) fulfillment of quantum parallel transport of a complete basis, (2) a concept of mixed state orthogonality adapted to unitary evolution, and (3) a normalization condition. We provide a method for computing the off-diagonal mixed state phases to any order for unitarities that divide the parallel transported basis of Hilbert space into ... Downloads: 10 | |

| Noncyclic mixed state phase in SU(2) polarimetry - Peter Larsson We demonstrate that Pancharatnam's relative phase for mixed spin$-{1/2}$ states in noncyclic SU(2) evolution can be measured polarimetrically. Downloads: 6 | |

| Comment on `Detecting non-Abelian geometric phases with three-level $Λ$ systems' - Marie Ericsson In their recent paper, Yan-Xiong Du et al. [Phys. Rev. A 84, 034103 (2011)] claim to have found a non-Abelian adiabatic geometric phase associated with the energy eigenstates of a large-detuned $\Lambda$ three-level system. They further propose a test to detect the non-commutative feature of this geometric phase. On the contrary, we show that the non-Abelian geometric phase picked up by the energy eigenstates of a $\Lambda$ system is trivial in the adiabatic approximation, while, in the exact tr... Downloads: 6 | |

| Off-diagonal mixed state phases in unitary evolution - Erik Sjöqvist Off-diagonal mixed state phases based upon a concept of orthogonality adapted to unitary evolution and a proper normalisation condition are introduced. Some particular instances are analysed and parallel transport leading to the off-diagonal mixed state geometric phase is delineated. A complete experimental realisation of the off-diagonal mixed state geometric phases in the qubit case using polarisation-entangled two-photon interferometry is proposed. Downloads: 7 | |

| Off-diagonal quantum holonomy along density operators - Stefan Filipp Uhlmann's concept of quantum holonomy for paths of density operators is generalised to the off-diagonal case providing insight into the geometry of state space when the Uhlmann holonomy is undefined. Comparison with previous off-diagonal geometric phase definitions is carried out and an example comprising the transport of a Bell-state mixture is given. Downloads: 9 | |

| Off-diagonal geometric phase for mixed states - Stefan Filipp We extend the off-diagonal geometric phase [Phys. Rev. Lett. {\bf 85}, 3067 (2000)] to mixed quantal states. The nodal structure of this phase in the qubit (two-level) case is compared with that of the diagonal mixed state geometric phase [Phys. Rev. Lett. {\bf 85}, 2845 (2000)]. Extension to higher dimensional Hilbert spaces is delineated. A physical scenario for the off-diagonal mixed state geometric phase in polarization-entangled two-photon interferometry is proposed. Downloads: 11 | |

| Measuring Pancharatnam's relative phase for SO(3) evolutions using spin polarimetry - Peter Larsson In polarimetry, a superposition of internal quantal states is exposed to a single Hamiltonian and information about the evolution of the quantal states is inferred from projection measurements on the final superposition. In this framework, we here extend the polarimetric test of Pancharatnam's relative phase for spin$-{1/2}$ proposed by Wagh and Rakhecha [Phys. Lett. A {\bf 197}, 112 (1995)] to spin $j\geq 1$ undergoing noncyclic SO(3) evolution... Downloads: 13 | |

| Effect of intersubsystem coupling on the geometric phase in a bipartite system - X. X. Yi The influence of intersubsystem coupling on the cyclic adiabatic geometric phase in bipartite systems is investigated. We examine the geometric phase effects for two uniaxially coupled spin$-{1/2}$ particles, both driven by a slowly rotating magnetic field. It is demonstrated that the relation between the geometric phase and the solid angle enclosed by the magnetic field is broken by the spin-spin coupling, in particular leading to a quenching effect on the geometric phase in the strong coupling... Downloads: 11 | |

| Adiabatic Approximation for weakly open systems - Patrik Thunström We generalize the adiabatic approximation to the case of open quantum systems, in the joint limit of slow change and weak open system disturbances. We show that the approximation is ``physically reasonable'' as under wide conditions it leads to a completely positive evolution, if the original master equation can be written on a time-dependent Lindblad form. We demonstrate the approximation for a non-Abelian holonomic implementation of the Hadamard gate, disturbed by a decoherence process... Downloads: 6 | |

| Robustness of the adiabatic quantum search - Johan Åberg The robustness of the local adiabatic quantum search to decoherence in the instantaneous eigenbasis of the search Hamiltonian is examined. We demonstrate that the asymptotic time-complexity of the ideal closed case is preserved, as long as the Hamiltonian dynamics is present. In the special case of pure decoherence where the environment monitors the search Hamiltonian, it is shown that the local adiabatic quantum search performs as the classical search. Downloads: 6 | |

| The quantum adiabatic search with decoherence in the instantaneous energy eigenbasis - Johan Åberg In Phys. Rev. A {\bf 71}, 060312(R) (2005) the robustness of the local adiabatic quantum search to decoherence in the instantaneous eigenbasis of the search Hamiltonian was examined. We expand this analysis to include the case of the global adiabatic quantum search. As in the case of the local search the asymptotic time complexity for the global search is the same as for the ideal closed case, as long as the Hamiltonian dynamics is present... Downloads: 9 | |

| Manifestations of quantum holonomy in interferometry - Erik Sjöqvist Abelian and non-Abelian geometric phases, known as quantum holonomies, have attracted considerable attention in the past. Here, we show that it is possible to associate nonequivalent holonomies to discrete sequences of subspaces in a Hilbert space. We consider two such holonomies that arise naturally in interferometer settings. For sequences approximating smooth paths in the base (Grassmann) manifold, these holonomies both approach the standard holonomy... Downloads: 7 | |

| Adiabatic geometric phases in hydrogenlike atoms - Erik Sjöqvist We examine the effect of spin-orbit coupling on geometric phases in hydrogenlike atoms exposed to a slowly varying magnetic field. The marginal geometric phases associated with the orbital angular momentum and the intrinsic spin fulfill a sum rule that explicitly relates them to the corresponding geometric phase of the whole system. The marginal geometric phases in the Zeeman and Paschen-Back limit are analyzed... Downloads: 7 | |

| Holonomy for Quantum Channels - David Kult A quantum holonomy reflects the curvature of some underlying structure of quantum mechanical systems, such as that associated with quantum states. Here, we extend the notion of holonomy to families of quantum channels, i.e., trace preserving completely positive maps. By the use of the Jamio{\l}kowski isomorphism, we show that the proposed channel holonomy is related to the Uhlmann holonomy. The general theory is illustrated for specific examples... Downloads: 8 | |

| Non-Abelian generalization of off-diagonal geometric phases - David Kult If a quantum system evolves in a noncyclic fashion the corresponding geometric phase or holonomy may not be fully defined. Off-diagonal geometric phases have been developed to deal with such cases. Here, we generalize these phases to the non-Abelian case, by introducing off-diagonal holonomies that involve evolution of more than one subspace of the underlying Hilbert space. Physical realizations of the off-diagonal holonomies in adiabatic evolution and interferometry are put forward. Downloads: 9 | |

| Non-Abelian quantum holonomy of hydrogen-like atoms - Vahid Azimi Mousolou We study the Uhlmann holonomy [Rep. Math. Phys. 24, 229 (1986)] of quantum states for hydrogen-like atoms where the intrinsic spin and orbital angular momentum are coupled by the spin-orbit interaction and subject to a slowly varying magnetic field. We show that the holonomy for the orbital angular momentum and spin subsystems is non-Abelian, while the holonomy of the whole system is Abelian. Quantum entanglement in the states of the whole system is crucially related to the non-Abelian gauge str... Downloads: 8 | |

| Nodal free geometric phases: Concept and application to geometric quantum computation - Marie Ericsson Nodal free geometric phases are the eigenvalues of the final member of a parallel transporting family of unitary operators. These phases are gauge invariant, always well-defined, and can be measured interferometrically. Nodal free geometric phases can be used to construct various types of quantum phase gates. Downloads: 10 | |

| Open system effects on slow light and electromagnetically induced transparency - Jonas Tidström The coherence properties of a three-level $\Lambda$-system influenced by a Markovian environment are analyzed. A coherence vector formalism is used and a vector form of the Lindblad equation is derived. Together with decay channels from the upper state, open system channels acting on the subspace of the two lower states are investigated, i.e., depolarization, dephasing, and amplitude damping channels... Downloads: 3 | |

| Unifying Geometric Entanglement and Geometric Phase in a Quantum Phase Transition - Vahid Azimi Mousolou Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are respectively the real and imaginary parts of a complex-valued geometric entanglement, which can be investigated in typical quantum interferometry experiments. We argue that the singular behavior of the complex-value geometric entanglement at a quantum critical po... Downloads: 10 | |

| Three-qubit topological phase on entangled photon pairs - Markus Johansson We propose an experiment to observe the topological phases associated with cyclic evolutions, generated by local SU(2) operations, on three-qubit entangled states prepared on different degrees of freedom of entangled photon pairs. The topological phases reveal the nontrivial topological structure of the local SU(2) orbits. We describe how to prepare states showing different topological phases, and discuss their relation to entanglement... Downloads: 12 | |

| Universal Non-adiabatic Holonomic Gates in Quantum Dots and Single-Molecule Magnets - Vahid Azimi Mousolou Geometric manipulation of a quantum system offers a method for fast, universal, and robust quantum information processing. Here, we propose a scheme for universal all-geometric quantum computation using non-adiabatic quantum holonomies. We propose three different realizations of the scheme based on an unconventional use of quantum dot and single-molecule magnet devices, which offer promising scalability and robust efficiency. Downloads: 7 | |

| Operational approach to the Uhlmann holonomy - Johan Aberg We suggest a physical interpretation of the Uhlmann amplitude of a density operator. Given this interpretation we propose an operational approach to obtain the Uhlmann condition for parallelity. This allows us to realize parallel transport along a sequence of density operators by an iterative preparation procedure. At the final step the resulting Uhlmann holonomy can be determined via interferometric measurements. Downloads: 11 | |

| Berry phase and fidelity susceptibility of the three-qubit Lipkin-Meshkov-Glick ground state - Erik Sjöqvist Berry phases and quantum fidelities for interacting spins have attracted considerable attention, in particular in relation to entanglement properties of spin systems and quantum phase transitions. These efforts mainly focus either on spin pairs or the thermodynamic infinite spin limit, while studies of the multipartite case of a finite number of spins are rare. Here, we analyze Berry phases and quantum fidelities of the energetic ground state of a Lipkin-Meshkov-Glick (LMG) model consisting of t... Downloads: 8 | |

| Robustness of non-adiabatic holonomic gates - Markus Johansson The robustness to different sources of error of the scheme for non-adiabatic holonomic gates proposed in [New J. Phys. {\bf 14}, 103035 (2012)] is investigated. Open system effects as well as errors in the driving fields are considered. It is found that the gates can be made error resilient by using sufficiently short pulses. The principal limit of how short the pulses can be made is given by the breakdown of the quasi-monochromatic approximation... Downloads: 4 | |

| Correlation induced non-Abelian quantum holonomies - Markus Johansson In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the L\'{e}vay geometric phase [2004 {\it J... Downloads: 3 | |

| Generalization of geometric phase to completely positive maps - Marie Ericsson We generalize the notion of relative phase to completely positive maps with known unitary representation, based on interferometry. Parallel transport conditions that define the geometric phase for such maps are introduced. The interference effect is embodied in a set of interference patterns defined by flipping the environment state in one of the two paths. We show for the qubit that this structure gives rise to interesting additional information about the geometry of the evolution defined by th... Downloads: 4 | |

| Mixed state geometric phases, entangled systems, and local unitary transformations - Marie Ericsson The geometric phase for a pure quantal state undergoing an arbitrary evolution is a ``memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution not only depends on the geometry of the path of the system alone but also on a constrained bi-local unitary evolution of the purified entangled state... Downloads: 12 | |

| Non-adiabatic holonomic quantum computation - Erik Sjöqvist We develop a non-adiabatic generalization of holonomic quantum computation in which high-speed universal quantum gates can be realized by using non-Abelian geometric phases. We show how a set of non-adiabatic holonomic one- and two-qubit gates can be implemented by utilizing optical transitions in a generic three-level $\Lambda$ configuration. Our scheme opens up for universal holonomic quantum computation on qubits characterized by short coherence times. Downloads: 32 | |

| Kinematic approach to off-diagonal geometric phases of nondegenerate and degenerate mixed states - D. M. Tong Off-diagonal geometric phases have been developed in order to provide information of the geometry of paths that connect noninterfering quantal states. We propose a kinematic approach to off-diagonal geometric phases for pure and mixed states. We further extend the mixed state concept proposed in [Phys. Rev. Lett. {\bf 90}, 050403 (2003)] to degenerate density operators. The first and second order off-diagonal geometric phases are analyzed for unitarily evolving pairs of pseudopure states. Downloads: 13 | |

| Geometric phases for mixed states in interferometry - Erik Sjöqvist We provide a physical prescription based on interferometry for introducing the total phase of a mixed state undergoing unitary evolution, which has been an elusive concept in the past. We define the parallel transport condition that provides a connection-form for obtaining the geometric phase for mixed states. The expression for the geometric phase for mixed state reduces to well known formulas in the pure state case when a system undergoes noncyclic and unitary quantum evolution. Downloads: 1 | |